This paper presents a comparative overview of the most important approaches presented to address the behavioral modeling of microwave and wireless power amplifiers (PAs). Starting from a theoretical framework of recursive and nonrecursive nonlinear filters, it proposes a classification of the various PA behavioral models, discussing their abilities to represent the different effects observed in practical circuits. Using that formal procedure, one explains how it was possible to integrate a wide range of behavioral modeling activities and to show that some of them, which at first glance seemed to be quite different, are, indeed, identical in their modeling capabilities.

A comparative overview of microwave and wireless power-amplifier behavioral modeling approaches

A comparative study of nonlinear behavioral models with memory for radio-frequency power amplifier (PAs) is presented. The models are static polynomial, parallel Hammerstein (PH), Volterra, and radial basis-function neural network (RBFNN). Two PAs were investigated: one was designed for the third-generation (3G) mobile telecommunication systems and one was designed for the second-generation (2G). The RBFNN reduced the total model error slightly more than the PH, but the error out of band was significantly lower for the PH. The Volterra was found to give a lower model error than did a PH of the same nonlinear order and memory depth. The PH could give a lower model error than the best Volterra, since the former could be identified with a higher nonlinear order and memory depth. The qualitative conclusions are the same for the 2G and 3G PAs, but the model errors are smaller for the latter. For the 3G PA, a static polynomial gave a low model error as low as the best PH and lower than the RBFNN for the hardest cross validation. The models with memory, PH, and RBFNN, showed better cross-validation performance, in terms of lower model errors, than a static polynomial for the hardest cross validation of the 2G PA

A comparative analysis of behavioral models for RF power amplifiers

This paper proposes a system-level behavioral model for RF power amplifiers (PAs), which exhibit memory effects, that is based on the parallel Wiener system. The model extraction is performed using two-tone intermodulation distortion (IMD) measurements with different tone frequency spacings and power levels. It is found that by using such a model, more accurate adjacent-channel power-ratio levels may be predicted for high PAS close to the carrier frequency. This is validated using IS-95B CDMA signals on a low-power (0.5 W) class-AB PA, and on a high-power (45 W) class-B PA. The model also provides a means to quantify memory effects in terms of a figure-of-merit that calculates the relative contribution to the IMD of the memoryless and memory portion of the PA nonlinearity. This figure-of-merit is useful in providing an estimate of the amount of correction that a memoryless predistortion system may have on PAS that exhibit memory effects.

Quantifying memory effects in RF power amplifiers

This paper proposes a system-level behavioral model for RF power amplifiers (PAs) that exhibit memory effects. PAs with memory effects are shown to have two-tone intermodulation distortion (IMD) levels that vary depending on tone-spacing. Thus, typical single tone extracted AM/AM and AM/PM characteristics cannot accurately model PA memory effects. By varying the frequency spacing of two-tone signals, envelope frequency dependent transfer functions can be derived. Using these transfer functions, a behavioral model is developed which is based on the parallel-cascade linear and nonlinear (LN) system. This model gives more accurate results in predicting the behavior of PAs with memory effects close to the carrier frequency. The model is validated by comparing the predicted and measured adjacent channel power ratio (ACPR) of a CDMA signal amplified by a high power class-AB PA. It is found that the parallel cascade model improves ACPR prediction accuracy by as much as 4 dB compared to the single tone derived memoryless model.

Extraction of accurate behavioral models for power amplifiers with memory effects using two-tone measurements

Accurate system level simulation is indispensable for efficient RF communication system design. However system level models of nonlinear circuits are today very limited by their inability to handle nonlinear memory effects. The paper describes a new approach of system-level modeling which accounts efficiently for nonlinear envelope memory effects of wideband amplifiers, multipliers and mixers.

H. B. Poza

Papers

A wideband data link computer simulation model